# SimPEG.maps.ParametricLayer#

class SimPEG.maps.ParametricLayer(mesh, **kwargs)[source]#

Mapping for a horizontal layer within a wholespace.

This mapping is used when the cells lying below the Earthâ€™s surface can be parameterized by horizontal layer within a homogeneous medium. The model is defined by the physical property value for the background ($$\sigma_0$$), the physical property value for the layer ($$\sigma_1$$), the elevation for the middle of the layer ($$z_L$$) and the thickness of the layer $$h$$.

For this mapping, the set of input model parameters are organized:

$\mathbf{m} = [\sigma_0, \;\sigma_1,\; z_L , \; h]$

The mapping $$\mathbf{u}(\mathbf{m})$$ from the model to the mesh is given by:

$\mathbf{u}(\mathbf{m}) = \sigma_0 + \frac{(\sigma_1 - \sigma_0)}{\pi} \Bigg [ \arctan \Bigg ( a \bigg ( \mathbf{z_c} - z_L + \frac{h}{2} \bigg ) \Bigg ) - \arctan \Bigg ( a \bigg ( \mathbf{z_c} - z_L - \frac{h}{2} \bigg ) \Bigg ) \Bigg ]$

where $$\mathbf{z_c}$$ is a vectors containing the vertical cell center locations for all active cells in the mesh, and $$a$$ is a parameter which defines the sharpness of the boundaries between the layer and the background.

Parameters
meshdiscretize.BaseMesh

A discretize mesh

indActivenumpy.ndarray

Active cells array. Can be a boolean numpy.ndarray of length mesh.nC or a numpy.ndarray of int containing the indices of the active cells.

slopefloat

Directly define the constant a in the mapping function which defines the sharpness of the boundaries.

slopeFactfloat

Scaling factor for the sharpness of the boundaries based on cell size. Using this option, we set a = slopeFact / dh.

Examples

Attributes

 nP Number of model parameters the mapping acts on; i.e 4 shape Dimensions of the mapping

Methods

 Derivative of the mapping with respect to the input parameters. Return model parameters as a dictionary.
 layer_cont

## Galleries and Tutorials using SimPEG.maps.ParametricLayer#

Maps: Parametric Block in a Layer

Maps: Parametric Block in a Layer

Maps: Parametrized Layer

Maps: Parametrized Layer

Heagy et al., 2017 Casing Example

Heagy et al., 2017 Casing Example